Two-body continuum states in noninteger geometry

Christensen, E.R.; Garrido, E.; Jensen, A. S.

doi:10.1103/physreva.105.033308

Cited by 4 publications

(9 citation statements)

References 34 publications

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“…In this sense, the results provided in Ref. [17] for two-body systems were found to have universal character. The appearance of the twobody effective range as the length unit to be used to get universality is consistent with additional findings at the three-body level, where the two-body effective range is also found to be the relevant length scale unit setting a universal value for the three-body parameter [45].…”

Section: Universalitymentioning

confidence: 71%

“…In Ref. [17] two-body systems were discussed analytically for non-integer dimensions and general short-range potentials. The method was to refer numerical calculations to use of a square-well potential, where its radius, r 0 , and depth, V 0 , are found by the conditions that the ratio between the scattering length and effective range in three dimensions is identical to the same ratio for the given short-range potential.…”

Section: Universalitymentioning

confidence: 99%

“…( 11 Following what is done in Ref. [17] for two-body systems, and taking the z-axis along the squeezing direction, we interpret the hyperradius ρ in the d-space, as the hyperradius in the three-dimension space, ρ, but deformed along the z-axis by means of a scale parameter, s (see [15] for details):…”

Section: A Scaling and External Fieldmentioning

confidence: 99%

“…Furthermore, phase shifts in the spherical dmethod involve finite, and in general non-integer, effective angular momentum, where the realizable deformed external field has no angular momentum barrier. It is then remarkable that the d-method phase shift is equal to the phase difference between the two equivalent threedimension two-body wave functions calculated with and without short-range interaction [17].…”

Section: Introductionmentioning

confidence: 99%

“…The d-method has so far only been applied to bound states, which, by definition, fall off exponentially with increasing relative distance. However, very recently the method has been extended to two-body continuum states, where wave functions, scattering lengths, phase shifts, and cross sections are computed [17]. This extension is far from trivial, since the wave functions now extend their oscillations to infinity in the non-confined directions.…”

Section: Introductionmentioning

confidence: 99%

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Three-body continuum states and Efimov physics in noninteger geometry

2022

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Continuum structures of three short-range interacting particles in a deformed external one-body field are investigated. We use the equivalent d-method employing non-integer dimension, d, in a spherical calculation with a dimension-dependent angular momentum barrier. We focus on dimensions close to the critical dimension, d = dE, between two and three, defined by zero two-body energies, where the Efimov effect can occur. We design for this dimension region a schematic, longdistance realistic, square-well based, three-body spherical model, which is used to derive analytic expressions for the wave functions, scattering lengths, phase shifts, and elastic scattering cross sections. The procedure and the results are universal, valid for all short-range potentials, and for large scattering lengths. We discuss the properties and validity of the derived expressions by means of the simplest system of three identical bosons. The derived expressions are particularly useful for very small energies, where full numerical calculations are often not feasible. For energies where the numerical calculations can be performed, a good agreement with the analytic results is found. These model results may be tested by scattering experiments for three particles in an equivalent external deformed oscillator potential. The cross sections all vanish in the zero-energy limit for d < 3 with definite d-dependent power of energy.

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Section: Universalitymentioning

confidence: 71%

Section: Universalitymentioning

confidence: 99%

Section: A Scaling and External Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three-body continuum states and Efimov physics in noninteger geometry

2022

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Confinement of N-Body Systems and Non-integer Dimensions

Garrido,

Jensen

2024

Few-Body Syst

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The squeezing process of a three-dimensional quantum system by use of an external deformed one-body oscillator potential can also be described by the d-method, without external field and where the dimension can take non-integer values. In this work we first generalize both methods to N particles and any transition between dimensions below 3. Once this is done, the use of harmonic oscillator interactions between the particles allows complete analytic solutions of both methods, and a direct comparison between them is possible. Assuming that both methods describe the same process, leading to the same ground state energy and wave function, an analytic equivalence between the methods arises. The equivalence between both methods and the validity of the derived analytic relation between them is first tested for two identical bosons and for squeezing transitions from 3 to 2 and 1 dimensions, as well as from 2 to 1 dimension. We also investigate the symmetric squeezing from 3 to 1 dimensions of a system made of three identical bosons. We have in all the cases found that the derived analytic relations between the two methods work very well. This fact permits to relate both methods also for large squeezing scenarios, where the brute force numerical calculation with the external field is too much demanding from the numerical point of view, especially for systems with more than two particles.

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Electric charge controls plasmodesma conductivity

Howell,

Christensen,

James

et al. 2024

Preprint

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While plant cells are enclosed by rigid cell walls that counteract intracellular hydrostatic pressure1, their plasma membrane, cytosol, and endoplasmic reticulum (ER) remain connected through plasmodesmata, nanoscopic cell wall pores2. Plasmodesmal cell-to-cell transport occurs in the cytosolic sleeve between the plasma membrane and the ER membrane3–5, and is generally thought to be limited by the size of the moving particle alone6. Given that biological membranes carry negative electric surface charges7–9, this steric notion conflicts with physical theory of ion diffusion in nanometer-sized pores with charged walls10. Quantifying the movements of differently sized and charged fluorescent dyes inTradescantiastamen hairs, we found that anionic fluorophores of up to 1 kDa traversed plasmodesmata whereas much smaller cationic ones did not. While this agrees with theoretical expectations of different size exclusion limits for cations and anions, it questions current dogma concerning plasmodesma function and also structure, as it implies positively rather than negatively charged surfaces within plasmodesmal pores. Our findings call for re-evaluations of current models of symplasmic transport, especially of charged molecules like the phytohormone auxin (indole-acetic acid) and certain amino acids.

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Two-body continuum states in noninteger geometry

Cited by 4 publications

References 34 publications

Three-body continuum states and Efimov physics in noninteger geometry

Three-body continuum states and Efimov physics in noninteger geometry

Confinement of N-Body Systems and Non-integer Dimensions

Electric charge controls plasmodesma conductivity

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